In the vector control strategy of permanent magnet synchronous motors, issues such as maximum torque-to-current ratio control and field-weakening control are involved. The most popular and easy-to-understand explanation of the problem of field-weakening control is the way of current limit circle and voltage limit ellipse (circle ) . The figure below is the block diagram of the permanent magnet synchronous motor vector control.
In the case of determining the DC bus voltage UDCU_{DC}, the maximum stator voltage UsmaxU_{s max} that the inverter can output is certain. When the voltage UsmaxU_{s max} on the AC output side of the inverter reaches its maximum value, it will also cause the saturation of the current inner loop regulator. In order for the permanent magnet synchronous motor to obtain a wider speed adjustment range , it needs to be controlled by field weakening when it is running at a high speed above the base speed .
The idea source of PMSM (Permanent Magnet Synchronous Motor) field weakening control still comes from the field regulation control of separately excited DC motors.
When the terminal voltage of the separately excited DC motor reaches the maximum voltage, only by adjusting the excitation current of the motor, and then changing the excitation flux, the motor can run at a higher speed with constant power under the condition that the maximum output voltage remains unchanged.
In other words, separately excited DC motors can achieve the purpose of field weakening and speed expansion by reducing the field current . For PMSM, the excitation magnetomotive force cannot be adjusted due to the generation of permanent magnets, and the voltage balance during high-speed operation can only be maintained by adjusting the stator current, that is , increasing the stator direct-axis demagnetization current component . To achieve the purpose of magnetic field-weakening expansion.
1. Restricted by the rated output current of the inverter and the thermal rating of the motor itself, when the PMSM operates stably, the maximum magnitude of the current vector is IsmaxI_{s max}. The current vector can be expressed as:
is2=iq2+id2<ismax2i_{s}^{2} =i_{q}^{2} +i_{d}^{2} <i_{smax}^{2}
It can be seen from the above formula that the current vector can only run in a circle with the origin as the center and the radius of the maximum magnitude of the current vector in the coordinate system , which is called the current limit circle.
2. Limited by the power supply voltage on the DC side of the three-phase inverter, the voltage on the AC output side is also limited. When the PMSM operates stably, the voltage vector amplitude is:
us2=uq2+ud2<usmax2u_{s}^{2} =u_{q}^{2} +u_{d}^{2} <u_{smax}^{2}
(Ld⋅id+ψf)2+(Lq⋅iq)2≤(Usmax/ωr)2(L_{d} \cdot i_{d} +\psi _{f} )^2+(L_{q}\cdot i_{q})^2\leq (U_{smax}/\omega _{r})^2
Among them, UsmaxU_{s max} is the maximum value of the specified sub-terminal phase voltage. Under normal SVPWM modulation, Usmax=UDC/3U_{s max} =U_{DC} /\sqrt{3} , and when overmodulated, Usmax=2UDC/πU_{s max} =2U_{DC} /\pi , and UDCU_{DC} is the DC bus voltage. When the motor is a salient pole permanent magnet synchronous motor, Ld≠LqL_{d} \ne L_{q} . The equation represents a series of concentric ellipses that shrink toward the center point as the speed increases .
Of course, when the motor is a secluded pole permanent magnet synchronous motor, it represents a series of concentric circles that shrink toward the center point as the speed increases. In this way, when the motor works in the field weakening area, the stator current and terminal voltage will be limited by the following two conditions at the same time:
|is|≤ismax\left| i_{s}\right| \leq i_{smax} ,|us|≤usmax\left| u_{s}\right| \leq u_{smax} , we draw the equations satisfying these two conditions in a coordinate system as:
So where is the field weakening work area?
That is, in the red line area from B to C in the figure, iq gradually decreases in this area, and id gradually increases in the opposite direction. At this time, id plays the role of demagnetization, and the motor speed will gradually increase.
When the flux linkage generated by the permanent magnet of the permanent magnet synchronous motor and the orthogonal axis inductance Ld, Lq are determined, the electromagnetic torque T e of the motor depends on the stator current vector is. The magnitude and phase of is depend on id and iq. So as long as id and iq are controlled, the torque of the motor can be controlled. Certain speed and torque correspond to certain id and iq. Compare the current actual value and the given value of the motor respectively to realize its speed and torque control. And id and iq are independently controlled, which facilitates the realization of various advanced control strategies.
Generally, in the permanent magnet synchronous motor vector control, the motor is controlled by the principle of maximum torque current ratio (MTPA) below the base speed . Above the base speed, we use field-weakening speed regulation to control.
———————————————————————————————————
@pollux xie asked in the comment area , the relationship between iq, id and Te in the block diagram.
The block diagram I posted is a block diagram of the built-in PMSM vector control . The electromagnetic torque of the built-in permanent magnet synchronous motor satisfies the following formula:
People who look carefully may find that Te∗T_{e}^{*} in the block diagram is not TeT_{e}, what is Te∗T_{e}^{*}? is the per unit value of the electromagnetic torque. As for how to calculate the per unit value, you must first determine the base value, as follows:
At this point, the formula for the per unit value of the electromagnetic torque can be obtained:
Te∗=iq∗⋅(1−id∗)T_{e}^{*} =i_{q}^{*} \cdot (1- i_{d}^{*} )
The previous question said that below the base speed of the permanent magnet synchronous motor, the current is controlled according to the principle of maximum torque/current .
Especially for the built-in PMSM, the saliency effect can be used to obtain a higher torque/current ratio, reduce the volume of the permanent magnet, and reduce the flux of the permanent magnet, which can not only reduce the cost of the motor but also facilitate the weak field operation of the motor. We can get the relationship between the maximum torque and the two current components.
You can get iq=f(Te∗)i_{q} =f(T_{e}^{*} ) and id=f(Te∗)i_{d} =f(T_{e}^{*} ) in the block diagram
Attachment: The principle block diagram in the article comes from the reference.